Geometric Forms

Name: Image Gallery of Geometric Forms - Geometry Calculator
Author: Jürgen Kummer

This is an image gallery in which all geometric shapes on this site are presented in an overview, arranged like in the menu. Click on one image to go to the corresponding calculator. With these, the properties of each form can be calculates.

Regular Polygons

Other Polygons

Round Forms

Platonic Solids

Archimedean Solids

Catalan Solids

Johnson Solids

Cupolae: triangular, square and pentagonal cupola

Other Polyhedrons

Round Forms

Steinmetz Solids: Bicylinder and Tricylinder

On these pages you will find several hundred calculators and sketches for geometric forms. They are initially sorted by dimensions, whereas most forms are of course two- and three-dimensional. Within a dimension, the categories are sorted in such a way that straight forms are listed first, then curved ones, i.e. those that contain at least one bend. Finally, for straight forms, regular forms are listed first, then irregular forms. There are several degrees of regularity for three-dimensional straight forms.
Within straight forms, the sorting is done according to the number of corners or edges. In general, the well-known and common forms are listed first, but care is also taken to ensure that similar forms are close to one another. There are no official names for some of the more complicated forms and those composed of other forms; here, names were chosen that describe the corresponding form as well as possible.
The one-dimensional forms contain the helix as the rear entry, which actually only has one dimension, but extends in three dimensions. The Koch curve, which is also included there, is one-dimensional as it can be calculated here, but in its theoretical form with an infinite number of iterations it is a fractal with more than one but less than two dimensions. The two-dimensional forms contain the digon and the spherical triangle as the last entries, elements from spherical geometry. These are actually two-dimensional, but extend in three dimensions, namely on a sphere. Four-dimensional (and higher-dimensional) forms only exist in mathematics, not in our reality.

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